MinT - Best Known (58−24, 58, s)-Nets in Base 4

Best Known (58−24, 58, s)-Nets in Base 4

(58−24, 58, 98)-Net over F₄ — Constructive and digital

Digital (34, 58, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 29, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(58−24, 58, 1423)-Net in Base 4 — Upper bound on s

There is no (34, 58, 1424)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 83522 068287 255720 383969 999357 134615 > 4⁵⁸ [i]